The short answer in no, BUT of course plugin paid version usually have features that could help you do some stuff in a much easier, hassle free way.

For example Yoast SEO paid plugin comes with an internal linking tool for WordPress that makes internal linking process much faster and easier than doing it by hand, link by link.

I think a clear comparison is that of the washing machine. The washing machine does not make your clothes cleaner than if you washed them by hand; it simply allows you to obtain the same result with less effort and greater efficiency.

Obviously, if you are lazy, incapable or don’t have time to wash clothes by hand, the washing machine is a nice to have and it will do a better job than you would, but the maximum level of cleanliness achievable will always be the same.